Michael is 2 times as old as Stephanie. Fifteen years ago, Michael was 7 times as old as Stephanie. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Stephanie. Let Michael's current age be $m$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $m = 2s$ Fifteen years ago, Michael was $m - 15$ years old, and Stephanie was $s - 15$ years old. The information in the second sentence can be expressed in the following equation: $m - 15 = 7(s - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = m / 2$ . Substituting this into our second equation, we get: $m - 15 = 7($ $(m / 2)$ $- 15)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 15 = \dfrac{7}{2} m - 105$ Solving for $m$ , we get: $\dfrac{5}{2} m = 90$ $m = \dfrac{2}{5} \cdot 90 = 36$.